BROOMTOWN: Nick Swisher leaps on top of the Yankees' on-field celebration after they eliminated the Twins with a 4-1 win last night in Minnesota, setting up an ALCS showdown with the Angels. Photo: NY POST/Charles wenzelberg

MINNEAPOLIS — Alex Rodriguez wrapped his dock rope of a left arm around Derek Jeter’s neck and let out a howl right before the best player in pinstripes showered the smartest in champagne.

A 4-1 victory over the pesky Twins in Game 3 of the ALDS had propelled the Yankees into the ALCS that starts Friday night in The Bronx against the Angels.

Shortly after the sweep, bedlam broke out in the clubhouse, which is barely bigger than a suburban two-car garage. Though some Yankees fans believe it’s their birth right to win the World Series every year, the players understand the difficulty of winning and advancing.

And a big reason was Rodriguez, who supported a pitching gem by Andy Pettitte with an opposite-field homer to right-center in the seventh off Carl “American Idle” Pavano that tied the score 1-1. Jorge Posada’s opposite-field homer two batters later put the Yankees ahead 2-1.

“We didn’t hit except for Alex, collectively,” general manager Brian Cashman said of his club that batted .225 for the series and forgot Jeter hitting .400 (4-for-10).

Without Rodriguez, it wouldn’t have been that high. He went 5-for-11 (.455) with two homers and six RBIs in three games.

The Yankees are in the ALCS for the first time since 2004, when they won the first three games against the Red Sox and flushed the final four.

Of course, Rodriguez had help. Jeter made an intelligent play in the eighth that cut down Nick Punto rounding third on Denard Span’s infield hit behind second. Knowing he didn’t have a chance at the fast Span at first, Jeter spotted Punto rounding third and threw to Posada. With Punto on his way back to third, Posada fired a strike and caught Punto by plenty.

Then there was Pettitte, who retired the first dozen Twins before Michael Cuddyer ripped a single to left leading off the fifth. Pettitte gave up a run in the sixth, but left two on.

When he fanned Jason Kubel to open the seventh, Joe Girardi replaced Pettitte with Joba Chamberlain. Considering Pettitte had allowed a run, three hits, a walk, fanned seven and threw 81 pitches, it was a bold move.

“Delmon Young had success (9-for-14; .643 coming into the game) against Andy,” Girardi said of the move to Chamberlain. “I thought it was time to go to Joba. We liked the match up. My gut told me to go to Joba.”

Chamberlain was greeted by Young’s double, but retired the next two batters.

Enter Phil Hughes, whose postseason struggles continued when Punto opened the eighth with a double. Hughes was bailed out by Jeter’s play behind second. After he retired Orlando Cabrera on a fly to center, Girardi called for Mariano Rivera. He broke Joe Mauer’s bat on a ground out that ended the frame.

When Rivera walked off the mound the Yankees led 2-1. When he took it for the ninth, the advantage was 4-1 thanks to consecutive bases-loaded singles by Posada and Robinson Cano off Joe Nathan, who inherited a bases-loaded, one-out jam thanks to three walks.

Rivera recorded the final three outs for his MLB-record 35th postseason save.

So now it’s the Angels, who eliminated the Yankees in the first round in 2002 and 2005 and whose “Marbles In The Bathtub” style of offense has given the Yankees fits.

“We are good enough to get through this round,” Jeter said. “Now it gets more difficult, Anaheim has a great team. This series we couldn’t have played better.”